Probability

Question

Find the value of the probability of the standards normal variable Z corresponding to the shaded area under the standards normal curve.

1. P(Z<1.45)

2. P(Z>1.11)

3. P(0.3<Z<1.83)

4. P(Z>2.27)

Answer 1

Make sure you have a table for the standard normal distribution handy when reading this explanation.  The values in the table represent the probability that Z is less than or equal to that value.

 

1.  If you look up Z = 1.45 on the table, you should get 0.9265.  Therefore, 0.9265 is the probability that Z is less than or equal to 1.45, which is exactly what we need for this problem, so the answer is 0.9265

 

2.  If you look up Z = 1.11 on the table, you should get 0.8665.  This represents the probability that Z is less than or equal to 1.11.  We need the probability that Z > 1.11, so we just need to do 1 - 0.8665, which is 0.1335.

 

3.  To figure out the probability that Z is between two numbers, look up the bigger number, then look up the smaller number, then subtract the two results.  The bigger number will tell you the likelihood that Z is less than or equal to 1.83.  But this includes the region where Z < 0.3, so we'll need to subtract off that region to get the area in between.  For Z = 1.83, you get 0.9664, and for Z = 0.3, you get 0.6179.  This gives you 0.9664 - 0.6179, which is 0.3785.

 

4.  Simply look up 2.27 on the table (0.9884), then since you have a greater than symbol, do 1 - 0.9884 to get 0.0116.